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On the uniform representation of mathematical data structures

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Design and Implementation of Symbolic Computation Systems (DISCO 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 722))

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Abstract

Topics about the integration of the numeric and symbolic computation paradigms are discussed. Mainly an approach through a uniform representation of numbers and symbols is presented, that allows for the application of algebraic algorithms to numeric problems. The p-adic construction is the basis of the unifying representation environment. An integrated version of the Hensel algorithm is presented, which is able to perform symbolic and numeric computations over instances of ground (concrete) and parametric structures, and symbolic computations over instances of abstract structures. Examples are provided to show how the approach outlined and the proposed implementation can treat both cases of symbolic and numeric computations. In the numeric case it is shown that the proposed extension of the Hensel Algorithm can allow for the exact manipulation of numbers. Moreover, such an extension avoids the use of simplification algorithms, since the computed results are already in simplified form.

This work has been partially supported by Progetto Finalizzato “Sistemi Informatici e Calcolo Parallelo” of CNR under grant n. 92.01604.69.

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Authors and Affiliations

  1. Dipartimento Informatica e Sistemistica, Università “La Sapienza”, Via Salaria 113, I-00198, Roma, Italy

    Carla Limongelli & Marco Temperini

Authors
  1. Carla Limongelli
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  2. Marco Temperini
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Alfonso Miola

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© 1993 Springer-Verlag Berlin Heidelberg

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Limongelli, C., Temperini, M. (1993). On the uniform representation of mathematical data structures. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1993. Lecture Notes in Computer Science, vol 722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013186

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  • DOI: https://doi.org/10.1007/BFb0013186

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57235-0

  • Online ISBN: 978-3-540-47985-7

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